If you want to share a database, you really need to use a database management system, like SQL Server or MySql - Access, SQLite, or SQLCE are not good at multi-user working.
That means that you need to install a version of SQL Server on a PC that is "visible" to all the other PC's on the LAN, and make your software access the DB via that.
That's not complicated, but it is far too much to explain in a little text box like this!
Start here:
http://www.dotnetperls.com/sqlclient[
^] - it does a fair job of getting you started.